zero divisor

Short definition from Wiktionary

Noun

1. 1
   An element a of a ring R for which there exists some nonzero element x ∈ R such that either ax = 0 or xa = 0.
2. 2
   A nonzero element a of a ring R for which there exists some nonzero element x ∈ R such that either ax = 0 or xa = 0.